Question

* * * {LAST QUESTION; MEDAL} * * *

A study of one thousand teens found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 15 hours. The population standard deviation is 2 hours. What is the 95% confidence interval for the mean?

14.88−15 hours

14.88−15.12 hours

15−15.12 hours

14.76−14.24 hours

Answer 1

I cant help but here is someone who might be able to: @hartnn

Answer 2

Do we have an Empirical Rule?

You may wish to try two standard deviations on either side of the mean.

Answer 3

Yes, 68% at 1 and -1
95% at 2 and -2
99.7% at 3 and -3

But for 95% from the standard deviation, i got 11 and 19, which isn't one of the options..?

Answer 4

Have you considered that it wants the interval of the MEAN? You may wish to use \(SD_{Mean} = \dfrac{2}{\sqrt{1000}}\)

Answer 5

15 = 2/31.6227
What do I do with this?

Answer 6

How did you get 11-19?

It's the same thing, just with the right Standard Deviation.

Answer 7

What is the right standard deviation? Sorry, I don't understand.

Answer 8

Did you miss \(SD_{Mean}\) that I supplied, above?

Answer 9

No, but I just don't know what to do with that. It would be 2^15?

Answer 10

Reset!!!! How did you find 11-19? EXACTLY what did you do to get that?

Answer 11

Add and subtract the SD from both sides of the mean.

Answer 12

What was I supposed to do?

Answer 13

Why not just do that again?

You used \(SD_{Population} = 2\)

Do it again with \(SD_{Mean} = \dfrac{2}{\sqrt{1000}}\)

Answer 14

oh, like add/subtract 30 from both sides?

Answer 15

No, the Standard Deviation of the Mean is \(\dfrac{2}{\sqrt{1000}} = 0.0632455532\)

Where are you getting 30?

Answer 16

I multiplied 2 and 15.
So on the right side, I add 0.063 and subtract that number on the left? From the mean?

Answer 17

Why are you doing ANYTHING with 2 after calculating the Standard Deviation of the Mean?

The center of your confidence interval is 15. Never change that.
The Standard deviation is 0.0632455532.

Go!

Answer 18

Ok this is just confusing, sorry.....so,
15.0632, 15.1264, 15.1896 on the left side
14.9368, 14.8736, 14.8104 on the right?

Answer 19

Oh I see now. Thx for the help.